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The Motional Electric Field
New Horizons In Electric, Magnetic & Gravitational Field Theory
by
William J. Hooper(B.A., M.A., Ph. D. (University of California Berkeley); President & Director of Research, Electrodynamic Gravity, Inc.; Professor of Physics Emeritus, Principia College.)
_______________________________________________
Table of Contents
Appendix
This book is dedicated to Mr. And Mrs. Warren W. Gibson, who have made it possible financially to carry on the last two years of fruitful experimental work. The devotion and dedication of Mrs. Gibson (Fran) to this project, serving as secretary and Research Assistant, has provided a flame which has kept it aglow to its present status.
"It appears to me, that the study of electromagnetism in all its aspects has now become of the first importance as a means of promoting the progress of science." (James Clerk Maxwell: Treatise on Electricity & Magnetism, Vol. 1, Pref., p. vii.)
Nearly everyone believes that gravity is a force emanating from matter, but just how, just why, nobody seems to know! In the science of physics much is known about electricity and magnetism, but of gravity, nothing really, with the exception of the inverse square law of Sir Isaac Newton, which we know gravity obeys.
This treatise presents newly discovered unique and startling properties of one of our induced electric fields. It gives this field a new status among our field forces. Its unusual properties are possessed only by gravity. While it is too early to claim complete identification of this field and the gravitational field, the similarities are amazingly alike.
Electricity and Magnetism were once two separate sciences. In 1820, Hans Christian Oersted observed that magnetic flux was always looped about a current-carrying conductor. This discovery served to unite the two sciences of Electricity and Magnetism into one, that of Electromagnetism.
During World War II the writer, working on an invention for a "drift and ground speed meter for aircraft", arrived at a plan for utilizing the vertical component of the earth's magnetic field. If the voltage induced between the ends of two oriented linear conductors traveling horizontally across the vertical component could be measured within an aircraft, a self-contained meter, independent of ground instrumentalities, would be forthcoming. The plan was reviewed by the U.S. Bureau of Standards, and its workability confirmed under a certain restriction. It was stated that the device would be inoperable within a conducting cavity such as a metal-clad aircraft. Our textbbooks have taught us that when a linear conductor moves with a velocity V across a magnetic flux of intensity B, an electric field of vector intensity VxB is induced within the wire and gives rise to a voltage at its terminals. This electromagnetically induced electric field, often called a motional electric field, we have been taught, would be electrostatic in character, that is, identical and indistinguishable from an electric field arising from charges of electricity. We know that radio tubes, silvered on the inside, shield the interior from stray electrostatic fields. In the same way, it was explained, such a drift and ground speed meter within a metal-clad aircraft would be shielded from the electric field induced in a conductor by motion across the vertical component of the earth's magnetic field. This explanation was a jolt to the writer. How could we know, without experimental evidence, that such would be the case? This presented a great challenge! Some of the foremost thinkers in physics were consulted. It was discovered that there was no experimental evidence to support the popular belief held by physicists that the motionally induced V x B field was electrostatic in its fundamental character and therefore subject to shielding. It will be shown how, step by step, the writer has been guided over a period of 20 years to experimental means which at last reveal experimentally, beyond all doubt, the beautiful unique properties of the motional electric field. It is not electrostatic! Its immunity to shielding, magnetic or electrostatic, is the exciting property which it shares with the gravitational field and thereby indicates their kinship. By a general theorem in electric field theory we know that a non-uniform B x V field must also act attractively on matter! Thus the motional electric field has acquired a status which makes it quite unique.
Guided by theory the inventor has built a generator of the B x V field which projects its field into the surrounding space. The writer calls this artificially generated field Electrodynamic Gravity because it simulates gravity. Although utilizing principles of magnetic field superposition and electromagnetic induction, the product field, B x V, like the gravitational field displays no evidence that magnetism plays a part in its generation. Likewise it is free of electrostatic characteristics. Although magnetic flux is moved by the generator, there are no mechanically moving parts.
The guiding concept employed by the inventor was first set forth in 1957 by E. G. Cullwick (Electromagnetism & Relativity, p. 245, Longsman Green & Co.). His research had led him to the conviction that the magnetic flux loops discovered by Oersted were actually in motion along the linear conductor in the direction of the electron current giving rise to it, and moved with the electron drift velocity. Our motional electric field generator demonstrates the correctness of the foregoing prediction. Its operation makes use of this movement of flux to generate the B x V field in space about the generator. This confirmation of Cullwick's prediction is an experimental contribution to modern electronic theory and it has all the earmarks of being the welding link which ties gravitation to electricity and magnetism. The oersted flux, first its discovery, and now the discovery that it moves with the electron drift velocity giving rise to it, thus holds a unique role in the process of welding the three sciences into one.
The new generator affords useful instrumentation for directly measuring electron drift velocities in metals, as well as experimentally determining the number of electrons available at various temperatures. Thus, it provides a new experimental method f investigation into the realm dealt with by the Fermi-Dirac statistics. Theoretically, this device holds exciting possibilities of great utility at very low temperatures. If sufficiently intense fields can be obtained by the use of superconducting wire in our generator at low temperatures, as we have good reason to believe is possible, the phenomenon of attraction and polarization of materials by this field can be studied. This would immediately bring into the realm of possible experimental demonstration such effects as weightlessness, artificial gravity, and anti-gravitational effects. This achievement, the writer believes, will be no more difficult of attainment than that which has already been demonstrated experimentally.
Should success follow the forthcoming planned cryogenic (low temperature) experiments and we find that very intense B x V fields can be generated and identified with the gravitational field, the promise of utility to humanity would be beyond all description. Free electric power from the earth's gravitational field would be obtainable anywhere, under the sea, on earth or neighboring space, on the moon or the planets! Gravity-free laboratories on earth, and artificial gravity in spacecraft --- these are some of the possibilities! With such promises on the horizon it is difficult for the writer to rest on his oars for one minute. This treatise therefore goes forth with "Great Expectations!"
Sarasota, FL (December 1969)
New Horizons In Field Theory
Forty years have passed since Max Mason and Warren Weever wrote in their celebrated book, The Electromagnetic Field (1 ~ p. xii, Univ. of Chicago Press, 1929):
"The great scientific task of the next 50 years is the development of a new electromagnetic theory. It is impossible to forecast the form such a theory will take, so greatly are we prejudiced by our present views. It will, however, doubtless be based on a quantitative description of the individual behavior of charges"
The new physics under the leadership of such men as Einstein, Planck, Heisenberg, Schrodinger, and Bridgman, has produced a series of kaleidoscopic changes in classical concepts. The contributions of the first four of these five men have been well incorporated into our modern textbooks. It is the work of Bridgman, his philosophy as embodied in "The Logic of Modern Physics" (2 ~ MacMillan Co., 1928), and paraphrased as "The Operational Viewpoint", which has to a large extent inspired this treatise, and provided a beacon of illuminated thinking to guide contemporary physicists in the development of new ideas. What Bridgman has done is to show us how the advent of relativity theory has made it necessary to take cognizance of the fat that new phenomena spring into existence as the result of introducing into an experiment nothing more than motion or a change in motion. We must be aware of assuming that because of the fact that similarities exist between old and new phenomena that they are necessarily equivalent. To be specific, let us again turn to Mason and Weaver:
"It cannot be urged that it has been shown experimentally that moving particles and changing currents are rigorously equivalent as regards induced electromagnetic forces. It is very easy to let the notation carry the burden of the argument and to hold that the value of curl E s related to the rate of change of B in every case in the way stated by the equation (curl E = -?B/?t). It is very important to point out, however, that by doing so one may be overlooking something of fundamental physical importance." (3 ~ ibid., p. 257)
It is this "something of fundamental physical importance" which is overlooked when the so-called "principle of equivalence" is applied without rigorous examination and analysis. This is the very essence of Bridgman's thesis.
There is no evidence that the subject matter of electromagnetism, since its earliest inception, has ever been given the Bridgman treatment. If we desire to keep our future growth on solid scientific ground, we are faced with the necessity of review and revision of old and new concepts which dominate thinking in the direction of its inevitable expansion. We need much to learn how "greatly are we prejudiced by our present views". In order to make way for the next great breakthrough in physics we must first come face to face with facts that reveal how greatly our present concept of fields is restricting our thinking and limiting our achievements.
An example of one of the greatest blind spots in current popular field theory will illustrate this point. This blind spot, due to an assumed concept, has been upheld by some of our most brilliant mathematical physicists. So dogmatic and completely certain of the accuracy of his position was one that he contributed the following jingle with which to support his conviction:
"There is but one God Allah, And Mohammed is his prophet! There is but one electric field E, and Maxwell is its prophet!" (4 ~ J. Stepian, "Electrostatic or Electromagnetically Induced Electric Field?"; Scientific Paper 1451, Westinghouse Research Laboratory, 7-14-49)
That nature has provided us with but one field agency which accelerates electrons, one electric field, and that one electrostatic in its fundamental character, is perhaps the greatest of all our current prejudiced and erroneous views. None of Faraday's famous experiments show or prove the existence of but one electric field in nature. It is Maxwell's translation of these experiments into the language of mathematics that bear the tacit assumption of only one such field. But Faraday left us a word of warning:
"and considering the constant tendency of the mind to rest on an assumption, and, when it answers every present purpose, to forget that it is an assumption, we ought to remember that, in such cases, it becomes a prejudice, and inevitably interferes, more or less, with clearsighted judgment." (5 ~ Phil.Mag., 1844)
It will be shown with experimental and theoretical proof that this assumed and prejudiced view is incorrect. Indeed, it is as obsolete as the concept of the atom as being a single indivisible particle, and as obsolete as the concept of a single atom for each element. It is as unrealistic as were the arguments of the famous Professor Simon Newcomb, recipient of honorary degrees from ten European and seven American universities, who was demonstrating mathematically that man could not fly, while the Wright brothers were assembling their aircraft at Kitty hawk. Simply because it can be shown mathematically that an electrified particle will trace identical trajectories in each of two types of fields, is no proof that these fields, these accelerating agencies, are equivalent and identical. Penetrating properties of fields, rendering them immune to shielding, possessed by some and not by others, have no mathematical representation in such so-called proofs, hence the proof is not rigorous because it does not include all the field properties.
A second modern prejudice, an assumed concept, which has gained considerable popularity, is one which states "the whole concept of a magnetic field is a fiction." (6 ~ P. Moon & D.E. Spencer: "Electromagnetism Without Magnetism: An Historical Sketch"; Amer. J. Phys., vol. 22, p. 120, 1954)
By combining two conceptual prejudices, "one electric field" (or its equivalent, electric charges only) and "no magnetic field", Moon and Spencer have produced what they call "A New Electrodynamics" (7 ~ J. Franklin Inst. vol. 257: p. 369, 1954) which appears on the surface to have revamped the whole picture of electromagnetism, in which no reference is made of fields, and the formulation is in terms of charges and their motions only. It would appear upon first examination that the success of their endeavors would constitute a basis for establishing the verity of the two basic assumptions. But this is not the case, as will be shown. The Bridgman treatment of Maxwell's equations clarifies the paradoxes and ambiguities previously associated with them and in so doing it retains the intrinsic values found in electric and magnetic field concepts ( 8 ~ P. Moon & D.E. Spence: "Some Electromagnetic Paradoxes", J. Franklin Inst., vol, 260, p. 373, 1955). Both the Maxwell equations and the "New Electrodynamics" formulation take on new meanings when analyzed in the light of the Operational Viewpoint urged by Bridgman. We will go into this subject in the next chapter.
Wile Moon and Spencer claim that the complete elimination of all reference to electric and magnetic field concepts in their formulation brings it to "a closer contact with reality", to the writer, this constitutes rather a fleeing from the reality of fields by burying one's head in sand, like an ostrich, wherein only sand particles can be seen, and one's body remains in a variety of teeming dynamic forces.
The idea that magnetism may not have physical reality because electric currents which give rise to certain aspects of it may be replaced in the equations by moving charges has been given much consideration. Page and Adams in discussing elementary charge and the force equation state:
"It is often stated that no magnetic charges exist in nature, and that therefore the terms in ?H in this equation are without physical significance. On the contrary, we shall show that, if every elementary charged particle contains electric and magnetic charges in the same ratio, no electromagnetic experiment can reveal the value of ? --- therefore the field equation and the force equation become identical in form with the equations obtained on the assumption that only electric charge exists in nature. There is no experimental evidence, therefore, to justify the common assumption that only electric charges and no magnetic charges are present in the world of experience. If the reverse were true, or if electric and magnetic charges occurred combined in any fixed ratio, all electromagnetic phenomena would take place in exactly the same way. No electromagnetic experiment would reveal the proportions in which the two types of charge might exist." (9 ~ Leigh Page & Norman Adams: Electrodynamics, pp. 210-211, Van Nostrand & Co, 1940)
The concept of electric and magnetic fields possessing intensities and directions, susceptible to direct experimental measurement and mapping, is one of the most fundamental and elemental realities of electromagnetism. True it is that perplexing and incongruous problems in field theory, heretofor seemingly unsolvable, have plagued it, and indeed these problems are largely responsible for the current trend to avoid field theory, especially magnetic, wherever possible. It is right in this area that Bridgman's Operational Philosophy comes to our rescue and affords a solution which is both satisfying and illuminating.
Electric and magnetic fields are manifestation of force, and force is always associated with energy. Our understanding of the energy nature of electric and magnetic fields up to the present time appears clouded and uncertain. A clear adequate description has not been found by the writer in any contemporary text. In place thereof is found confusion worse confounded. In order to fully comprehend the significance of this treatise we must have some acquaintance with the present status of our knowledge of fields, both energy-wise and otherwise. A glimpse of this state of affairs may be gained from a few quotations from The Electromagnetic Field (10 ~ Mason & Weaver, op. cit., pp. 266-269). Speaking of the special density of electric and magnetic energy and of the Poynting Vector which measures the flux of energy at any point, we read: "The authors do not pretend to understand these concepts, but discuss them as adequately as they are able". They further say that they "are not able to ascribe any significance whatever to the phrase 'localized energy'". Nothwithstanding these views, they state, "The hypothesis of a spacially distributed electrostatic energy of volume density ha, however, played a large role in the development of electromagnetic theory" (11 ~ ibid., p. 162). And again, "in both electrostatics and magnetostatics, energy densities in space have, to be sure, been calculated" (12 ~ ibid., p. 269). It is an object of this treatise to completely clarify this area of electric and magnetic field energy.
Energy, in the many forms it assumes, appears today to play a leading role in the great drama of physical science. Whether it is kinetic or potential, mechanical, electric, magnetic, electromagnetic, binding energy of nuclear structure, or any other of its myriad manifestation, it is some form of energy, pure or bottled up in particle form, which we encounter and cognize at every turn in this physical world. Everything in the material universe is some form or manifestation of energy.
In the light of fundamentals it would seem most natural that a proper scientific description and classification of anything would include terms which reveal its energy nature, or status with respect to energy. In a comparison of one thing with another, one recognizes as a mere self-evident truism the fact that for any two things to be identical in nature, they must necessarily be identical from an energy standpoint, and this truism especially applies to force fields, both electric and magnetic.
This treatise will especially concern itself with one of the most important underlying properties of one of our electric fields, the "motional electric field B x V" and its immunity to shielding. It will present new theoretical and experimental knowledge which must have consequences of vital importance to the science and philosophy of modern physics. The picture presented will be based entirely upon conceptions of electromagnetic theory which are found in complete agreement with experiment. This picture, it is believed, will reveal not only the cause of many of our difficulties, but the way out of them. It will reveal a vista of new opportunities for research. It is confidently believed that as a result of the clarified picture thus attained, new horizons in field theory are in the offing. A glimpse of these horizons, together with an electromagnetic theory of gravitation leading up to the derivation of Newton's Inverse Square Law, will be presented with experimental proposals for its verification. Finally the subject of antigravity will be discussed and, in the light of this thesis, how a practical approach to this problem is clearly indicated with its thrilling possibilities.
Fundamental Fields
Webster defines science as "knowledge classified and made available in the search for truth". A correct classification of knowledge thus becomes the basic foundation of a science. The word classification has been underlined by the writer, because of its great importance. A wrong classification of anything can result in greatly impeding the progress of the branch of science in which it exists. Thus great treasures in science can be hidden and obscured for ages until some prospector comes along and reveals its true nature. A critical survey of the present status if electrodynamics reveals a considerable number of electric and magnetic fields which are brought into being by operations which are unique and seemingly unrelated. So entrenched is the present tacit assumption of physicists that nature has provide nature with one and only one electric field and one and only one magnetic field that no pioneer has as yet attempted to seriously penetrate this prejudice and venture into the possibilities of classification which might bring law and order to some of our current problems.
The advent of relativity theory was instrumental in forcing physicists to reexamine and alter many of their most cherished and fundamental concepts in physics. Consdier, for instance, the concept of time. None other than the great Sir Isaac Newton has defined time, in his Principia, in the following manner:
"Absolute, True, and Mathematical Time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called Duration."
Bridgman points out with great clarity that f we examine the definition of absolute time in the light of experiment, we find nothing in nature with such properties. By example after example he points out that many of the stumbling blocks which have clogged the progress of physics, and then he does something about it. He has contributed what is called the Operational Viewpoint as a guiding beacon to enable us to avoid making these kinds of mistakes in the future. In brief, he tells us what we should define and classify our concepts in terms of the operations which are necessary in order to detect and measure them, and not in terms which have no counterpart reality in nature, no direct experimental evidence to support them. Only as we do this, he points out, can we avoid treacherous pitfalls and embarrassments in the future growth of our science. He states, "It is evident that if we adopt this point of view toward concepts, namely that the proper definition of a concept is not in terms of its properties but in terms of actual operations, we need run no danger of having to revise our attitude toward nature. For if experience is always described in terms of experience, there must always be correspondence between experience and description of it, and we need never be embarrassed, as we were in attempting to find in nature the prototype of Newton's absolute time" (13 ~ Bridgman, op. cit., p. 6). While stating that "operational thinking will at first prove to be an unsocial virtue", he nevertheless predicts that, "In this self-conscious search for phenomena which increase he number of operationally independent concepts, we expect to find a powerful systematic method directing the discovery of new and essentially important physical facts" (14 ~ ibid., p. 224).
The writer has classified operationally the three most prominent electric and the three most prominent magnetic fields which we find in nature. They are as follows:
Fundamental Electric & Magnetic Fields (m.k.s. units)
(1) Ec = Qr/4 pi eor3
The electrostatic or Coulomb field arising from the presence of charges
(2) Em = v x Bs
The motional electric field which acts on charges traveling with velocity V across a magnetic induction Bs. This field is produced by flux cutting and should not be confused with Et arising from flux linking
(3) Curl Et = ?B/?t
or Et = ?A/?t
The electric field Et, in this formula arises from flux linking, or transformer electromagnetic induction discovered by Henry and Faraday. In this field B changes intrinsically with time. A is the magnetic vector potential.
(4) Curl Hs = J
This magnetostatic field H arising from a conduction current density J within a conducting medium was first discovered by Oersted. It is at rest with respect to the current circuit source producing it.
(5) Hm = -v x Dc
The motional magnetic field arising from relative velocity v with respect to electric charges producing the electric induction Dc.
(6) Curl HR = ?Dc/?t
The magnetic field HR surrounding a changing electric induction called a displacement current. This magnetic field plays a prominent part in the production of electromagnetic radiation. It was first theoretically predicted by Clerk Maxwell.
Particularly illuminating is the analysis of Cullwick with respect to the salient operational differences in the sources of the three types of electric field Ec, Em and Et (15 ~ E. Geoffrey Cullwick: The Fundamentals of Electromagnetism, p. 285; Cambridge Univ. Press, 1949). In brief, he pictures them as follows.
All electromagnetic phenomena applied in electrical technology have, as their fundamental basis, the mutual forces experienced by electric charges, and we have seen that these arise in three ways:
Ec ~ Two charges experience mutual forces in virtue of their positions. This is the electrostatic force of attraction or repulsion.
Em ~ They experience additional forces in virtue of their velocities. Thence arise the forces experienced by a conductor carrying a steady current in a constant magnetic field, the forces between current-carrying conductors, and the induction of en emf in a conductor moving relatively to the source of a magnetic field.
Et ~ They also experience additional forces by virtue of their accelerations, from which arise the induction of an emf by transformer actions, and electromagnetic radiation of energy.
The thing we are especially interested in, in this thesis, is that each of these unique operations with charges brings into existence a new force field which will act upon charges of electricity to accelerate them. The intensity of an electric field is defined at a point as the force per unit of charge will be exerted. The great mistake of the past has been the assumption that each of the above accelerating agencies are, in their intrinsic physical natures, in every way equivalent and identical since they each produce the same end product, the acceleration of a charged particle. Now in my human experience I may desire to move across a lake in a boat. As accelerating agencies I may select several which are one unique: (a) a set of oars, (b) a sail, (c) an outboard motor, (d) an engine-driven air propeller.
There is no question with respect to the uniqueness of these agencies in spite of the fact that each one produces the same end result --- namely, a force on the boat. Because we cannot cognize directly the unique accelerating agencies in electrodynamics by means of the five physical senses, they have been assumed to be all alike in nature, in spite of the known fact that operationally they arise from manipulations which are as uniquely different as in the case of the three accelerating agencies applied to the movement of a boat.
Had Bridgman's Operational Theory been published at an earlier date, it is dubious that the present popular view of these electric and magnetic fields would be as they are. Why? Because the three electric and the three magnetic fields listed above are each one produced by operational means which are experimentally just about as different as they could possibly be. This fact alone should be sufficient to challenge complacency and initiate a searching investigation of the facts. Contrary to popular belief, each one of these fields is unique in nature. It is self-evident that each of these six fields requires unique operations necessary to produce, detect, and measure it. Both theoretical and experimental evidence will be presented to show that at least some of our conceptions of these fields are fundamentally misconceptions, and in these cases the misconceptions are due to the fact that these fields are unique in nature, each one possessing characteristic properties of is own which entitle it to a distinct identity in nature. This discovery must inevitably render a great service in clarifying the confusion existent in the present state of our knowledge, and afford new opportunities for research, new possibilities in applied physics and new horizons for a unified field theory. An analysis of the properties of these fields will next be considered so that their unique properties may be apparent.
Table 1 has been prepared to show the outstanding differences in the properties of each of the first three operationally different electric fields. The recognition of the uniqueness of each field is aided by a comparative study of these properties. The properties of the electrostatic field are well known and need no elaboration in this treatise. Scientific literature dealing with this field is replete with its well-known characteristics.
Table 1: Field Properties
Field Properties: (1) Spatially distributed energy; (2) ØE = ds ; (3) Curl E ; (4) ?ab E = ds
; (5) E =dV/ds Potential function ; (6) Behavior with respect to shielding; (7) Div. E ; (8) Poisson's fundamental law with respect to the interior of conductors; (9) In conductors carrying current; (10) Inverse square law; (11) Spatial nature of field; (12) Relation to charges in it; (13) Field dependence; (14) Functional dependence on velocity.
Electrostatic Field: Es ~ (1) KE2/8 pi ergs/cc; (2) = 0 always; (3) = 0 always; (4) a constant always; (5) Yes; (6) Can be readily shielded with conducting material; (7) = 4 pi p; (8) Obeyed; (9) Conductors always have a surface charge; (10) Yes; (11) Continuous throughout space it occupies; (12) Charges within it produce a distortion of the field; (13) A primary field independent of all other fields; (14) Intensity of electrostatic field in any reference frame is parabolic function of v/c.
The electric field induced by a changing magnetic vector potential: Et = -dA/dt ~ (1) KE2/8 pi ergs/cc ; (2)
/0 in general; (3) = -dB/dt; (4) Not a constant. Dependent on the path of integration; (5) No; (6) Can be shielded with sufficient thickness of shielding; (7) = 0 always; (8) Not obeyed; (9) Can drive a current without a potential drop along the wire; (10) No; (11) Continuous throughout space it occupies; (12) Charges within it do not distort the field; (13) Dependent upon another field; (14) ---.The motionally induced electric field: Em = V x B ~ (1) No spatially distributed energy; (2)
/0 in general; (3) = v x (v x B)/0 in general; (4) In a perfectly uniform B the value of the integral between 2 points a and b will not be dependent on the path, will be independent of it, but in general this will not be true; (5) May or may not be a potential function; (6) Immune to shielding; (7) = 0 always; (8) Not obeyed; (9) Can drive a current without a potential drop along the wire; (10) By special design yes in certain portions of field; (11) Only present at points where moving charges exist; (12) Charges within it do not distort the field at all; (13) Dependent upon another field; (14) Intensity of motional electric field in any reference frame is linear function of v/c.In order that the unique character of each of the electromagnetically induced fields may be understood, considerable discussion will be required in view of the fact that so many texts emphasize the similarity of these fields in certain instances and fail to point out the vital, outstanding differences in their fundamental properties, which make it impossible for them to be identical in nature. Some of these differences have been revealed in scientific literature (16 ~ G. I. Cohn: Electrical Engineering 63: 441, 1949; E. G. Cullwick: The Fundamentals of Electromagnetism, pp. 84-87, Macmillan Co., 1939; W.V. Houston: American Physics Teacher 7: 373, 1939; Page & Adams: American Physics Teacher 3: 57, 1935)) but do not as yet seem to be generally incorporated in our textbooks. Cohn, in particular, has rendered an outstanding contribution…
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different ways of expressing one and the same fundamental phenomenon is because it is basically incorrect. Not only are the two types of field Em and Et fundamentally different and each one unique in nature, but an examination of the Faraday Lay, E.M.F. = -dN/dt, reveals that this equation itself does not hold true in general. In other words, it has been shown that the flux linking with a closed circuit can be either partially or completely removed from the circuit without inducing any electromotive force whatsoever! 17 ~ G. I. Cohn: Paradoxes of Electromagnetic Induction; Thesis, Illinois Inst. of Technology Library)
This can be accomplished by a cleverly designed switching circuit, one version of which is shown in Figure 1. This illustrates the fact that the flux linking with a closed circuit may be changed by three different unique operations: (1) Flux cutting, (2) Flux linking caused by -dB/dt, where the source of B is intrinsically changed with time, and (3) A uniquely designed switching circuit. Only the first two sets of operations produces an emf. The third set of operations produces no emf and for this reason the present manner of presenting Faraday's Law is invalid. There are two unique operational methods of inducing an emf, and we should not endeavor to derive them from one simple mathematical expression -dN/dt, because this expression includes or implies operations which will not induce and emf. It is therefore obsolete! As Cohn and others have shown, there are actually two kinds of electromagnetic induction and in general case both types are involved and each must clearly be understood and differentiated from the other. That the flux linking law, attributed to Faraday, does not hold for his own Faraday-disk unipolar generator, which requires the flux cutting law for its correct descriptive behavior, is perhaps one of the most outstanding examples of how vitally unique and essential is the role of each law and each of the corresponding electric fields produced by these laws.
Figure 1
In the Faraday generator there is no time rate of change in the magnetic induction B, since it originates from a permanent magnet and is constant. The circuit can even be made so as to link with no flux whatsoever. In any case, there is no change of B with time. This very fact that all contemporary authorities (18 ~ Slater & Frank: Electromagnetism, p. 86, McGraw-Hill, 1947) on this subject have found it necessary to add the flux cutting law to the famous Maxwell equations in order to satisfactorily explain all cases of electromagnetic induction is itself indicative of the uniqueness of the electric field so produced.
Many of my colleagues have said that it was not difficult for them to distinguish fundamental differences in the Coulomb field Ec and the magnetically induced fields Et and Em, but they were unable to see any clearly defined difference between the Et and the Em field. Let us, therefore, discuss some of the most outstanding differences between these two fields.
What is our concept of an electric field? Most physicists will reply that it is a force which acts upon an electric charge and tends to accelerate it in a definite direction termed the direction of the field. With this concept in mind, let us analyze the two electric fields Et and Em.
In Figure 2 below is shown a cross-section of a long straight solenoid in which a gradually increasing current is flowing counterclockwise.
Figure 2
The uniformly distributed magnetic flux density B within this area is therefore increasing with time and according to Faraday's law of Electromagnetic Induction, the emf around any closed circuit placed wholly within the area shown in Figure 2 would be given by: emf = dN/dt = ?QEt-ds where N equals the total flux linking the circuit.
Our interest centers on Et, the electric field within the conductor of such a circuit, giving rise to the emf. Obviously, Faraday's Law gives us absolutely no information about this field Et other than to say that the line integral of this field around the closed circuit will give us a value of the emf induced in it. If this closed circuit A lies in the plane of the area, Figure 2, then at point P in this circuit, it is obvious that Et is directed toward the bottom of the paper. If, however, we select the circuit B instead of A, then at this same point P the electric field Et is directed horizontally to the right. If we select circuit C instead of B, we then find Et directed toward the top of the paper at P exactly the opposite direction from that in circuit A. And if we select circuit D then Et at P is directed horizontally to the left, in exactly the opposite direction that it had in circuit B. That an electric field Et exists in this area there seems to be no doubt since an emf arises within each of these circuits. But this field Et is very peculiar, since it is impossible to define it at the point P unless we first select a particular circuit through P which will then enable us to determine its direction at P.Now let us remove the conducting circuits from within the area of Figure 2, and place a stationary free charged particle Q at the point P. Will it move? If so, in what direction will it move? If it remains stationary, and is free to move, then does an electric field exist at this point? Certainly the magnetic flux density exists there and is changing with time, but we have no assurance whatsoever that it will act upon a stationary charge, nor is the direction in which it will act unless it is first given an initial velocity, or unless it is confined within the conducting medium of a closed circuit. No other electric field has this unique operational prerequisite, which in this case appears to require that the charged particle upon which it acts must either have an initial velocity within the electric field, or that it must exist within a conducting circuit before it will make itself manifest. A free stationary charged particle placed within an Em or Ec field will be immediately acted upon in both magnitude and definite direction. About all that we can say in a descriptive manner of Et at a point P, such as shown in Figure 2, is that this transformer type field has curl at that point, as shown by Maxwell's formula. For a clarifying conception of just what curl means one will find it helpful to study Skilling's treatment of it where he defines it as the limiting value of circulation per unit area (19 ~ H. H. Skilling: Fundamentals of Electric Waves, 2nd Ed., p. 41; J. Wiley & Sons, Inc, 1948). This means simply, as applied to Figure 2, that if a small conducting disk of ink, say a dot made with India ink, were placed at point P, negative electrons would circulate in this dot in a counterclockwise direction. The dot of ink would be everywhere at the same potential, and therefore uncharged. Curl is one of the most outstanding characteristics of the Et field which may or may not be possessed by the Em field, but never by Ec. Now place this same dot of India ink in a uniform Em field and it will become an electric dipole. The action of a uniform Et field on this dot is therefore very much different from that of an Em uniform field.
With the exception of mason and Weaver's text, little literature appears to exist which directs attention to the ambiguous nature of the concept of the spatial distribution of energy as concerns the two electromagnetically induced electric fields. That the electric field induced by a magnetic flux intensity which is changing with time has a spatial distribution of energy, whereas the motionally induce electric field does not have any such identical distribution of electric field in space is one of the most crucial of the fundamental differences in their properties. Since the establishment of this fact that these two fields differ radically in their relation to field energy is all-important to the objectives of this treatise, let us now take up a digression at this point.
Insofar as this writer is informed, no one questions the actuality of the special distribution of energy in the case of the electrostatic field or the Et field, due to a magnetic vector potential intensity varying with time (20 ~ The transformer law is usually stated in terms of the negative time ration of change of magnetic flux linking with the circuit and this gives the total induced emf. The electric field produced by this type of induction is most conveniently designated by the time rate of change of the magnetic vector potential.). Calculations involving field energy in the electrostatic case have long been made without difficulty, and the transfer of energy between the primary and secondary coils of a transformer without any movement of its component parts give direct evidence that electric energy is distributed in the space occupied by the Et field. The very nature of this electric field requires the concept of the spatial distribution of field energy.
An analysis of the nature of the motional electric field will reveal, on the other hand, that this concept of spatially distributed electric field energy, is not only required for a satisfying understanding of phenomena where this field is involved, but it actually induces basic ambiguities and impossible conceptions.
Let us now examine the origin and basic nature of the motional electric field with its unusual property.
Em = V x B. This vector field equation was derived by Lorentz from the empirical force formula of Biot and Savart. This is the electric field which is present in the moving wires constituting the armature coils of an electric generator. It causes an emf to exist in a conductor by virtue of motion across magnetic flux. Such induction is called a motionally induced emf or flux cutting emf. As we shall see, this field has some of the most unusual and interesting properties conceivable. Page and Adams have emphasized one of these unique properties. They point out in the case of the generator with a rotating armature coil that this field, "exists only in the moving conductor" --- where moving electric charges are present --- "since no electric field is present in the observer's reference frame" (21 ~ Page & Adams, op. cit., p. 16). Let us examine this aspect of the field more closely, for neither the electrostatic field nor the Et field possesses this property, for these fields can exist in an observer's reference frame, whether a conducting circuit, or conductor, or charge is at hand or not.
Three essential operational ingredients are necessary to bring this Em field into existence: (1) A constant magnetic induction B, (2) an electrically charged particle e (22 ~ the charged particle may be an electron in a piece of matter, or free as in a gas), a relative velocity v between the particle and the reference frame of the magnetic source producing B. A deflecting force will act upon the particle wherever it moves across magnetic flux lines. As viewed from the reference frame of the particle, this force (v x B) has many aspects of a real electric field and in fact it is termed a motionally induced electric field having an intensity (v x B) per unit charge. In the reference frame of the magnetic source giving rise to B only a magnetic field is present. One observes that the moving charge is acted upon by a force which to all appearances is wholly magnetic in nature. Whether we think of it as a deflecting magnetic force or an electric field, it is obvious that it exists only at the points in space where moving charges, either free or in matter, are present, for stationary electric charges are unaffected. In a vacuum, or in space between moving electric charges, no Em field or deflecting magnetic force exists. Hence it must necessarily have a spotty, or discontinuous nature. How can this be possible?
Let us proceed as Mason and Weaver have suggested by considering "a quantitative description of the individual behavior of charges". Let a positively charged particle with mass m and charge e be projected into a vacuum chamber with uniform velocity vo at right angles to the direction of uniform magnetic flux B. The particle has initial kinetic energy T = 1/2 m vo2. By Ampere's Law, the moving particle (or current element) is surrounded by a concentric distribution of magnetic flux.
Figure 3
It will be acted upon by a mechanical deflecting force F = e vo x B.
It will also be readily seen that this force on the charged particle exists only when there is a magnetic field about the particle. The force is actually the force of lateral repulsion between two magnetic fields. Without the presence of both magnetic fields, no such force exists, hence the existence of f requires the simultaneous presence of all three of its essential components, e, v and B. The actual action on the charged particle is magnetic in character, rather than electrical.
Let us next observe that the force f always acts at right angles to both v and B. Since the displacement of the particle is always in a direction at right angles to the force, this force can do no work on the charged particle upon which it acts, and no energy is extracted from B. This force, arising from the magnetic repulsion between two magnetic fields, one due to the moving particle, and the other due to the applied B, acts like a circular deflecting constraint or baffle, which only changes the direction but not the magnitude of the velocity of the particle. The speed of the particle and hence its kinetic energy remain unchanged. It is well known that such force will cause the particle to travel in a circular path, the radius of which is readily obtained by equating the force Bevo to the centrifugal force mvo2/r and solving for r, r = mvo/eB. The particle is thus trapped by the magnetic field, which will hold it to a circular path until its original kinetic energy is dissipated by collisions with neighboring particles, or by radiation.
It is of particular importance to this discussion and is again repeated, that since the deflecting force is always at right angles to the relative velocity vo of the particle and also to B, no work is done on the particle by the deflecting force.
Whether the particle is confined within the boundaries of a wire or not, (v x B) will always be at right angles to v and B. For clarification let us suppose the particle is enclosed within a frictionless tube the axis of which is at right angles to vo and to B. Few further impose the condition the velocity vo of the tube be kept constant in magnitude and direction. Let us examine the behavior of the particle within it. As the tube moves forward, the particle is prevented from moving in a circular path by the walls of the tube, but it can and will begin to move along the axis of the tube under the deflecting action of the magnetic field. To maintain the original forward component of its velocity vo constant, the external agency moving the tube will have to supply the particle with additional kinetic force in this direction.
As the particle acquires a velocity component vt along the axis of the tube, the resultant force v x B acquires two components, one along the tube, which will be constant (vo x B), and one at right angles to the tube (vt x B), opposing to the forward motion (Lenz's Law). We thus see the that the additional kinetic energy imparted to the charged particle moving down the tube is transmitted to the particle directly by the external force moving the tube. This kinetic energy is continuously channeled along the tube by the deflecting action of the magnetic induction B interacting with the magnetic field formed around the moving charged particle and the constraint of the tube itself.
The modus operandi of v x B is thus seen to be wholly magnetic in character. The conception of this force, when viewed from the standpoint of an observer at rest in the reference frame which is traveling with velocity vo, as being an electric field similar in character to that of an electrostatic field is therefore an artificial figment of the imagination which instead of clarifying the understanding of motional electromagnetic induction, often befogs it. The concept of v x B as an electric field is a convenient mathematical construct, however, for computing induced emf's, but the actual nature of the phenomenon with which one is dealing must be kept clearly in mind to avoid mistakes. The electromotive force induced between the terminals of a short straight linear conductor of length l moving with relative velocity across a magnetic induction B is given by the formula:
(Eq. 2) E = v x B • l
whereas that induced in a closed circuit is given by:
(Eq. 3) E = ? v x B • dl
and is often difficult to evaluate. In these formulae the term v x B represents the direction and magnitude of the fictitious electric field intensity em. The energy associated with this field is directly imparted to the charged particles by a mechanical prime mover which produces the relative velocity instead of by an actual electric field.
An important point in the foregoing analysis is that it serves to illustrate the fact that since the Em field is by its intrinsic nature only the repulsive force between two magnetic sources, that of B and that of the moving charge, it cannot exist except a those points where electric charges with magnetic fields about them exist. The Em field is only at those points where a magnetic field exists that can interact repulsively with the magnetic induction B.
Therefore, it is evident that there can be no continuous spatial distribution of Em electric field energy as there is in the case of the Eo or Et fields. Since no electric Em field exists in a space without charges, there is no Em field energy in a vacuum or in free space such as can exist with an electrostatic field. We need to remember this fact when we think of the Em field phenomenon from the viewpoint of a moving magnetic flux acting on a stationary electric charge. A single phenomenon when viewed from two different reference frames can appear to be fundamentally different, but such relative viewing does not alter the fundamental basic cause giving rise to it. Since the real basic nature of the v x B phenomenon has not hitherto been exposed in detail and hence is to a large extent currently taught and believed to be of an electrostatic nature by theoretical physicists, it will be worth our while to go into some of the subtle aspects it presents when it is so conceived.
Let us consider the popular view of this phenomenon as presented by most interpreters of relativity theory. The Special Theory of Relativity as applied to electrodynamics states that if we have a uniform electric field of intensity E, due to charges, and a uniform magnetic induction B, due to magnets, both at rest in a reference frame S, then in frame S' moving with uniform velocity v with respect to S an observer will find an electric intensity E', and a magnetic induction B' given in vector notation in absolute gaussian (c.g.s.) units by:
(Eq. 4) E' = ? {E - (1/c) v x B}
(Eq. 5) B' = ? {B - (1/c) v x E}
where ? = 1/? 1 - (v/c)2
and
c = 3 x 1010 cm/sec.
The current confusion among physicists is that many interpret relativity theory as showing that ? v x B/c
is an electric field, identical in nature to an electrostatic field. The reader will note that E' is the vector sum of two electric intensities, ?E
, which is an electrostatic field, and V(v x B)/c. Added in this manner, many physicists have tacitly assumed that E' and ?v x B/c
Winch in his excellent treatise states, "Notice that (v x B) is not an electrostatic field intensity for it is not due to a distribution of charges. We have shown that the line integral of electrostatic field intensity around any closed path is always zero and there is no exception in this case, i.e., the electrostatic field intensity set up by the displaced charges integrates to zero around any closed path. (v x B) is due to the motion of the conductor in the magnetic field, and an external agency is feeding energy into the system, and a net amount of work is done by a charge in moving completely around the circuit. Notice also the (v x B) does not exist in the absence of moving charges, because it is the magnetic force on the charges moving with the wire which sets up the electric field intensity" (25 ~ Ralph P. Winch: Electricity & Magnetism, p. 536; Prentice & Hall, Inc., 1955).
Notwithstanding such pronouncements, the writer has discussed the subject with many exponents of relativity theory who are quite insistent that all the terms in Equation (4) must be considered identical to, and indistinguishable from, an electrostatic field. A personal letter from a colleague at our National Bureau of Standards also takes this position, as well a several Nobel Laureates with whom he has consulted. And this stand is taken admittedly by these physicists without a single iota of direct experimental evidence with which to support it!
During the early stages of the work on this project, I called on several Nobel Laureates to discuss the worthwhileness of this endeavor, one of whom was the distinguished physicist and authority in the field of electrodynamics, Enrico Fermi, who had delivered a lecture at the 1944 Public Affairs Conference at Principia College. Among the questions asked, two will be of interest to the reader. (1) "If it were ever discovered that the motional electric field v x B/c was unique and not identical to, and indistinguishable from, an electrostatic field, would this discovery be of any great value to our scientific knowledge?" His answer in substance was: It would indeed be of very great significance and consequence. (2) "To your knowledge, do you know of the existence of any direct experimental evidence which confirms the belief that the motional electric field and the electrostatic field are identical in nature?" After considerable thought, his reply was, "Come to think of it, I can recall of no such existent evidence."
It will now be shown that the relativity equations themselves provide a means for obtaining a fuller understanding of the physical nature of the terms they contain. It is important to observe mathematically that in the general case every term of both of these equations (4) and (5) is a function of B where B = v/c. By a binomial expansion it can be readily shown that:
(Eq. 6) ? = [l + (l/2) ?2 + (3/?) ?4 + …]
Substitution in the two right hand terms of Equation (4) yields
(Eq. 7) Es = ? = [l + (l/2) B2] E
(Eq. 8) E'm = ? [v x B/c] = [l + (l/2) B2] (v x B/c) = BBn
where v and B are taken at right angles to each other and n is a unit vector at right angles to both v and B and terms of higher degrees that B2 have been dropped.
Equations (7) and (8) represent respectively the electrostatic, and the motional electric, field components of the resultant electric intensity E' in the reference frame S' moving with uniform velocity v with respect to S. If now E and B in reference frame S are adjusted so that they are both perpendicular to v and to each other and their intensities fixed at constant values such that:
E's -E'm = 0
Then these two electric field intensities will be equal in magnitude and opposite in direction (27 ~ Two large, similar, rectangular, parallel, and vertical plates separated by a distance d could be oppositely charged and electrically isolated in s. Above and below the air space between the condenser plates two large circular horizontal Helmholtz coils could next be fastened so that when connected in series a constant current through them would produce a uniform vertical magnetic induction B in the space between the condenser plates. Let S' be a frame of reference moving horizontally through this space with velocity v at right angles to both E and B.)
A stationary electron in S' will therefore experience no force acting upon it because the resultant electric intensity in this frame is zero. Most relativists claim that under this situation there will be complete cancellation of electric fields. It will be observed that E's and E'm are parabolic and linear functions of B respectively. It will at once be evident that although E's and E'm can be made equal to each other in magnitude and opposite in direction for any one reference frame S', moving with an assigned value of v and a fixed proper adjustment of E and B in frame S, such that v = cE/B, nevertheless such equality of E's and E'm would be possible for only two frames at the most, for a straight line can cut a parabola in not more than two points. It is thus self-evident that in the general case it would not be possible to make these two oppositely directed fields continuously equal in more than two possible reference frames at the most, by assigning fixed values to E and B in S. This is a clear-cut case of the simple superposition of two distinct types of fields. If the E'm term represented an electric field which is identical to and indistinguishable from an electrostatic field, then it would have to behave like one, which would require that it vary parabolically with ? instead of linearly. How could there be complete cancellation of fields in a particular frame if there is a real difference in their intensities manifest in the reference frames having both greater and lesser velocities than this particular frame? Surely such a situation calls for fields which are distinct and unique, balanced against each other with a zero resultant in one (or possibly two) particular frames, but not in neighboring frames of reference.
The (v x B)/c term most clearly simulates the characteristics of an electrostatic field when it is isolated by itself, without the presence of a resultant magnetic induction! It is this case which has been mostly responsible for the popular belief that the two fields are identical in nature. To simplify the picture, let us first assume a vertical uniform magnetic induction B in frame S and no electrostatic field present. In the reference frame S', moving with uniform horizontal velocity v, with respect to S, an observer will discover a horizontal electrical field, (v x B)/c and a vertical magnetic induction B' = B (assuming velocities small with respect to c), the path of a free electrified particle in frame S' under the action of the two fields which are at right angles to each other will be that of a cycloid traced on a horizontal plane. The path of the particle as seen in frame S would be circular, as previously shown. This motion projected on frame S' moving with velocity v, is that of a point on the circumference of a circle rolling in a horizontal plane along a line in the direction of -v. If we now superimpose a uniform magnetic induction B" equal in magnitude and opposite in direction to B', in frame S', then in this frame we will have only the isolated electric field v x B/c, with the resultant vertical magnetic induction of zero intensity. Now this electric field very greatly simulates that of an electrostatic field, and it is readily understandable that many physicists have so interpreted it. The path of the particle in this field is now rectilinearly in the direction of v x B/c in S', and parabolic as seen from S. Furthermore, since the curl and divergence of v x B/c in S' are both zero, as they are in the case of a uniform electrostatic field, mathematicians can call upon what is known as the identity theorem as a proof that the Em field is identical to an indistinguishable from an electrostatic field. This proof amounts to nothing more than saying that the dynamic behavior of a charged particle will be the same in both fields. In the following chapters we will show experimentally that this is not always true. Also analysis shows that a prime mover is required for moving the source of B" and supplies energy to the particle continuously.
Let us again analyze this case carefully because of its great importance. Kinetic energy is imparted to a free charged particle and gives it a velocity vo with respect to frame S. At the commencement of its motion the particle is at rest in frame S', which is moving with the same velocity. It appears to an observer in this frame that the particle starts from rest and begins to move in the direction of (vo x B)/c. If the magnetic induction is S' is only that due to B, then its motion v' with respect to S' will produce a new deflecting intensity v' x B'/c in frame S' in the direction of -vo. If, however, the equal and opposite magnetic induction B" is introduced in this frame, the effect would be to produce another deflecting intensity v' x B'/c which would be equal and opposite in direction to the intensity v' x B"/c. At this point one needs to think carefully. The deflecting intensity v x B'/c in S' directed against the forward motion of the particle arises by virtue of Lenz's Law. The force on the particle due to this intensity will act continuously as long as the particle moves at right angles to vo. To enable the particle to maintain constantly it original forward velocity vo, the kinetic energy which is being channeled at right angles to vo must be continuously replaced. To do this, work must be done continuously upon the magnet giving rise to B" in S', because the action of B" on the particle is to assist its forward motion with respect to S in exactly the same amount that v x B'/c depresses it. Two magnets are involved in this action. (1) The magnet giving rise to B' in S' and which is at rest in S. (2) The magnet giving rise to B" in S' and which must be continuously supplied with energy from a prime mover.
The particle can thus be made to travel rectilinearly in S', in the direction of (vo x B)/c provided energy is continuously given to it via the role played by B". This is the situation which appears on first inspection to be exactly like an electrostatic field. A free electron originally at rest in S' will be accelerated rectilinearly in S' at right angles to vo. The electron is seemingly without contact with any material body, hence the electric field (vo x B)/c appears to be the only source of its steadily accumulating kinetic energy. The energy would appear to have come from a spatial distribution also as in the electrostatic case, since (vo x B)/c is the only electric field present in S', and the resultant magnetic induction is zero. This appearance is exceedingly deceptive and is the basis of this current false assumption with respect to the motional electric field. No prime mover is required in the electrostatic case! The energy in this case comes from the field itself.
In the first place, we must remember that an electric field of the type (v x B)/c cannot of itself impart energy to the electron because its line of action is always normal to the velocity of the electron with respect to S, and to the direction of B. We will remember in one of our previous discussions, that this deflecting intensity was shown to channel the kinetic energy of the particle down a tube without itself imparting energy. The function of the tube actuated by a prime mover was to continuously supply to the particle the energy to so channel and prevent the particle from taking up a circular path in S or a cycloidal path in S'. We now discover that the superposition of a magnetic induction B" in S' accomplishes the same thing that the tube did. But this accomplishment can only be achieved by feeding energy to the particle continuously in the forward direction as the tube did and this is done by a prime mover acting on the magnet giving rise to B".This magnetic induction B" interacts with the magnetic field around the charged particle so as to continuously push the particle in the forward direction vo, thus replacing continuously the kinetic energy channeled at right angles by (vo x B)/c and thus keeping the velocity of the particle in this forward direction constant, thereby making its path in S' one that is wholly at right angles to vo. A prime mover gives kinetic energy to a magnet, and its magnetic field pushes on the magnetic field around the particle, and thus does work continuously, which in frame S' appears as increasing kinetic energy of the rectilinear motion of the charged particle. No magnetic field energy is used up in this transfer of energy to the particle. The magnetic field of the magnet is a physical part of the magnet which pushes against the magnetic particle with exactly the same force that the tube did in our earlier description. It performs the same function as that of the tube. There is no real electric field involved in this picture except that around the charged particle, which when moving (by Ampere's Law) gives rise to the magnetic field around it. Thus the whole action of an isolated (v x B)/c field on a charged particle, instead of being electrostatic has a description which is essentially the direct transfer of mechanical kinetic energy from prime movers to the particle. No spatially distributed motional electric field energy enters the picture of this field. The uniform and relative motion of two magnets with equal and oppositely directed fields and the presence of an electric charge released with kinetic energy from its position of rest in the reference frame of one of the magnets produces a combination of pushing and deflecting magnetic forces which causes the particle to behave as though it were in an electrostatic field. This should not surprise us. What should surprise is that physicists should have assumed, without direct experimental evidence, that these combined magnetic forces could be identical to and indistinguishable from an electrostatic field. A monkey and a man are two distinctly different agencies (we hope)! They can, however, exert identical forces on one and the same object, and if oppositely directed hold the object in equilibrium. But surely no one will use such an argument as evidence that a monkey is a man, or that a man is a monkey! Such, however, appears to be the nature of some arguments that (v x B)/c is intrinsically electrostatic. Cajori states: "The unscientific physical speculations of Aristotle held the world bound within their grasp for two thousand years; the unfortunate corpuscular theory of Newton controlled scientific thought for over a century" (28 ~ Florian Cajori: A History of Physics, p. 101, Macmillan Co., 1922).
It has taken over a century to pierce the fog created by the assumption of one, and only one, electric field by Maxwell. This assumption having served him well in formulating his beautiful electromagnetic equations, nevertheless became a prejudice, and interfered, more or less, with clear-sighted judgment.
The Electromagnetic Force Equation
Three outstanding electric field intensities when added together vectorially, constitute what has been termed the electromagnetic force equations (in kms unts):
(Eq. 9) E = Ec + Em + Et = Cr/4?eor3 + (B x V) - ?A/?t (29 ~ Cullwick, op. cit., p. 287)
In their A New Electrodynamics, Moon and Spencer derive a new formulation for this equation based entirely on the force between two charged particle Q1 and Q2 (30 ~ Moon & Spencer, op. cit., p. 369). These authors show that all possible electric intensities can be exerted by charge Q1 and Q2 due to (a) constant Q1, no relative motion, (b) constant Q1, uniform relative velocity, and (c) constant Q1, accelerated motion, when added become respectively:
(Eq. 10) E = Ec + Em + Et = F/Q2 = Q1r/4?eor3 + Dr Q1/4?eor2 (v/c)2 [1-3/2 cos2?] -aa Q1/4?eoc2r dv/dt
Note that the Coulomb intensity Ec is the same in (9) and (10). The motional intensity Em and the transformer intensity Et differ in form but represent in each of the two equations the same identical accelerating agencies. The outstanding difference between the two equations is that with (10), one can calculate electric intensities without having to entertain any field concepts, electric or magnetic! The authors claim considerable advantages for their formulation (10) over that of (9), and show five examples, each of which involves difficulties and incorrect answers if the classical Maxwell equations are employed indiscriminately, but which find correct answers in every instance with their formulation (10) (31 ~ P. Moon & D. E. Spencer: "On Electromagnetic Induction, J. Franklin Inst., vol. 260, p. 213, 1955). What they do not point out is that when the terms of (9) are applied in the same discriminating manner with respect to the operational aspects of the problems, as was (10), the ambiguities disappear and correct answers are forthcoming.
The Principle of Superposition as applied to fields, states that when several fields are superimposed on one another, each will act as though the others were absent. The simple addition of the separate terms in both (9) and (10), tacitly implies that this principle holds true in all cases. This tacit assumption in turn stems from the assumption that there is but one electric field, and each of the three terms being of this one nature, can be superimposed and added vectorially. If there was but one electric field in nature, then one would have to admit that the simple addition of these terms is scientifically correct. If, however, we have several unique electric fields in nature, each with its own unique physical properties, then the Principle of Superposition as applied to these fields is open to question. To illustrate this point, let us consider a case where we have only the two uniform Ec and Em fields present, superimposed so as to be equal in intensity, parallel, and oppositely directed. Equations (9) and (10) then reduce to:
(Eq. 11) E = Ec - Em = 0
It becomes obvious at once that if there is but one electric field in nature, then the resultant field is zero. If, however, each of these fields is unique, and a physical experiment can be so arranged as to permit only one to act, while the action of the other is restricted (due to their unique properties) then, in this case, the resultant field will not be zero as required by equation (11). If then we can arrange such a unique experiment which will pit these two agencies Ec and Em against each other equally, we will have a critical means whereby experiment alone, not assumption nor dogma, will give us a clear cut answer to the question of fields, and the application of the Principle of Superposition. It becomes obvious that nature alone can give us the answer to the questions we have raised. If in such an experiment the equation (11) is unambiguously not zero, i.e., if one field can be made to act alone, in the presence of the other, then this experiment will prove experimentally the spatial existence of unique electric fields, one of which is unique by virtue of electromagnetic properties not possessed by the other.
In the next chapter we will describe in detail experiments which answer the questions we have raised.
Experimental Confirmations by Electrostatic Shielding
In the first part of this chapter we will deal theoretically with the subject of shielding in order that the full significance of the experimental work to be described in the latter part may be transparent to the reader.
Among the properties of electric fields, there is no single one which more clearly characterizes the uniqueness of the electrostatic field, in contrast to the electromagnetically induced fields, than the singular behavior of this field with respect to shielding. In order that this phenomenon may be thoroughly understood, let us first review the electrostatic behavior and then contrast this with that of the other two electric fields. This behavior has been termed the fundamental law of electrostatics first stated by Poisson:
"The equilibrium distribution of the charges on conductors must be such that the force on any particle of electricity in the interior of a conductor, whether solid or hollow, is zero, since in a conductor electricity can move freely and the existence of a force on the particle will cause a flow of electricity. Thus, the equilibrium condition requires that all charge resides on the outside surfaces and that no charge or electric field whatsoever exist in the interior."
Physicists are well acquainted with the fact that the Et field, present in transformer coils, caused by a varying magnetic induction with time, does not obey this law at low frequencies, and only at high frequencies and with heavy shielding can this field even approach being effectively screened out. Since Poisson's law is a fundamental law, which applies to all electrostatic fields, it becomes evident at once that the Et electric field cannot and does not qualify as being electrostatic in character. This means that the Et electric field must be unique in nature. Although most physicists are willing to admit that this field, which arises from the growth or decay of a magnetic flux with time, is not electrostatic, nevertheless they cling tenaciously to the belief that there is only one electric field in nature (32 ~ Sleplan, op. cit.). Believing that the isolated motional electric field v x B/c has been shown mathematically to be electrostatic in character because teachers of relativity theory have taught this, it is not difficult to stretch the imagination a little further to include the Et field. We will, however, proceed to present direct experimental evidence which confirms the claim presented in this thesis that the isolated motional electric field is note and cannot be electrostatic in character. As we have seen, nevertheless, this field had deceptive aspects which cause it to resemble in many ways the electrostatic field.
In order that the case may be transparently understood, let us consider a very simple case of relative motion. Let us assume that we have an inertial system S which has only a uniform downward magnetostatic induction B, and no electrostatic field is present. In the inertial system S', which is moving with uniform horizontal velocity v with respect to S, the transformation equations (4) and (5) yield:
(Eq. 12) E' = ? (v x B)/c
(Eq. 13) B' = ? B
For convenience, let us think of the system S' as a completely closed rectangularly shaped coach, made of aluminum, traveling due North with velocity v. Let us think of B as the magnetic induction due to the earth's magnetic field (presumed vertical). The transformation equations (12) and (13) inform us that an observer riding in his car would find a vertical magnetostatic induction B', both inside and outside the car, which for ordinary speeds would be identical to B. This induction would be reduced to zero by building around and attached to the car a large Helmholtz coil which would produce within and throughout the car an equal but oppositely directed induction B". By doing so we isolate the electric field E' within the car. An observer would find outside the car a uniform electric field E', directed from East to West, given by (12). Within the car, however, we know from experience that an ordinary electric field intensity probe would register zero, or no resultant electric field intensity. According to most interpreters of the Special Theory of Relativity, this is exactly what should be expected, since they claim ?(v x B)/c is identical to, and indistinguishable from, an electrostatic field, and it must, therefore, behave similarly with respect to shielding. Hence, according to this view, the aluminum coach, being a good conductor, has produced within it in accordance with the fundamental law of electrostatics a surface redistribution of charge which brings about the complete cancellation of all electric field within the car so that no charge or electric field whatsoever exists inside the exterior bounding surface of the car.
An entirely logical and different conclusion may now be arrived at by reasoning based upon our known laws of electromagnetism. The car is moving across a magnetic induction B directed vertically downward. Therefore every free electron within the aluminum shield will experience a force due to the electromagnetically induced field ?(v x B)/c urging it toward the right hand side of the car. Under the influence of this field a redistribution of charge thus takes place until an electrostatic field Es directed horizontally across the inside of the car from the West wall to the East wall, equal in intensity and oppositely directed to the inducing field is established. When equilibrium is thus established, there will be within the car two oppositely directed coterminous electric fields, of types Ec and Em, in balance such as to produce a zero resultant electric intensity.
The question before us now is, which picture is correct? Can it be that Es and Em are actually identical in nature and complete cancellation within the car takes place? Experimental evidence must answer this question, and it does, clearly and decisively. Before presenting this answer, however, it will be of interest to note some of the comments made by physicists with respect to this question and the dense fog which has surrounded it. A colleague at the National Bureau of Standards, giving a view in harmony with most interpreters of relativity theory, has, in a letter, written with respect to the inside of the shield:
"If it is assumed that magnetic induction has a certain property not in conflict with anything observed experimentally, it follows that there are two electric fields which at every point are equal and opposite in direction. One of these fields results from electromagnetic induction and the other from electric charges.
"If it is assumed that magnetic induction has another property, not in conflict with anything observed experimentally, it follows that at no point is there an electric field and on no element of surface is there an electric charge. Therefore, any prediction not in accord with both of these assumptions should be considered as lacking an experimental basis.
Smythe, in commenting upon the problem of measuring ground speed in an aircraft by measuring the emf induced in a device by translation across the vertical component of the earth's magnetic field, states:
"The question arises as to whether the effect disappears if the apparatus is electrically shielded in the airplane. We know that the magnetic field will penetrate nonmagnetic metallic conductors, but we also know that the induced electromotive forces in the shields will set up electric fields tending to counteract the fields induced inside." (33 ~ William R. Smythe, Static & Dynamic Electricity, p. 500, McGraw-Hill, 1939)
Thus, S' finds his airplane in a transverse electric field, (v x B)/c. he cannot therefore use any metallic shields about his apparatus.
Here again we have the uncertain popular view among physicists as to whether Es and Em are in this case identically equivalent concepts which completely cancel each other. We will now show that this does not occur.
The Ironing Board Experiment ~ (34 ~ Egbert Jones & W. J. Hooper: Physics 401 Project, March 26, 1954, Principia College Library)
This crucial experiment was so named because the apparatus resembled somewhat an ironing board on wheels. The object of the experiment was to detect and measure the voltage induced in a test coil by the motional electric field Em while it was in a balanced and uncancelled state with an equal and oppositely directed electrostatic field Ec:
Figure 4: The Ironing Board Experiment
Three electrical circuits were employed, all lying in horizontal planes, parallel to a large laboratory lecture table. The test circuit consisted of a coil of 100 turns of #27 B&S gauge insulated copper wire wound in a groove on the 3/4" edge of a plywood form in the approximate shape of an ironing board 1' x 7' 4", as shown in the scale diagram Figure 4. The terminals of this coil were connected to a Leeds & Northrup Microvoltmeter which was mounted on the plywood form, which in turn was equipped with rubber-tire wheels so that it could be pulled at a uniform North-South velocity along the lecture table by an electric motor coupled to a reduction gar. The precise velocity was calculated with the use of a meter stick and an electric timer. Surrounding the forward end of the test coil, a second circuit was wound on a plywood extension consisting of a single strand of #16 B&S copper wire held at a constant two-inch distance from the test circuit, and carried a uniform direct current so adjusted that the magnetic flux B" surrounding it would exactly cancel out the vertical component B of the earth's magnetic field at the location of the test circuit. The third circuit was a largely accurately constructed Helmholtz coil so mounted in the laboratory and adjusted that the trailing end of the test circuit moved horizontally in the central region (between the two coils) in which the vertical component of the earth's field was completely cancelled. The entire test circuit including the microvoltmeter was electrostatically shielded. A very heavy coat of aquadag was applied over the test coil and the top and bottom of the supporting plywood frame. In addition, aluminum foil was wrapped around the forward semicircular part of the test coil, and finally put over the entire front portion of the apparatus. When moved uniformly along the table, the shielded wires of the test coil along the two sides of the frame move horizontally in the earth's magnetic meridian and therefore cannot cut any flux. The trailing edge of the test coil in the central region of the Helmholtz coil likewise can cut no flux. The forward end of the test coil alone cuts the vertical component of the earth's field, and is not at rest with respect to the canceling flux B" of the secondary circuit. The shield, with the exception of the portion within the Helmholtz coil, likewise cuts the vertical component of the earth's magnetic field. We now have a perfect set-up with which to test experimentally whether or not the uniform isolated motional electric field is equivalent and identical to the electrostatic field. The walls of the shield have induced in them an emf which drives electrons to the west side and leaves a positive charge on the east side of the shield. We know that these charges will build up until the electrostatic field caused by this separation of charge will be everywhere within the shield equal and opposite to the intensity of the motional electric field giving rise to it. If they are equivalent and identical in nature, they will completely cancel each other out and the leading wires of the test coil will be in a field-free space. If a voltage is induced in the test coil, it will be because these two fields do not cancel each other, because they are unique and different in their fundamental physical natures. Table II gives the results of 19 different velocities which were carefully measured:
Table II
Trial ~ Distance (cm) ~ Time (sec) ~ Velocity (cm/sec) ~ MicroV (observed) ~ MicroV (theory)
1 28.9 46.1 .626 10.5 10.3
2 20.0 28.2 .708 11.5 11.73 20.0 28.6 .699 11.5 11.54 20.0 31.3 .639 10.2 10.55 20.0 28.4 .704 11.2 11.66 20.0 30.1 .665 10.5 11.67 20.0 29.4 .680 11.0 10.98 20.0 29.0 .590 11.2 11.49 20.0 28.8 .698 11.3 11.510 20.0 31.1 .644 10.5 10.611 20.0 30.8 .651 10.5 10.712 20.0 30.7 .651 10.7 10.713 20.0 31.7 .632 10.7 10.414 20.0 32.1 .623 10.0 10.315 20.0 32.5 .615 10.2 10.216 20.0 32.5 .616 10.0 10.317 20.0 32.2 .623 10.1 10.318 20.0 32.0 .625 10.5 10.319 20.0 32.4 .618 10.0 10.2202.1 204.5Average Values: 10.64 10.76v = nvBl (volts; n = 100; B = .55 x 10-4 Webers/m2; l = .30 metersA brief account of two other shielding experiments carried out in the writer's laboratory to provide interesting qualitative demonstration equipment will now be described.
The Trapeze Experiment
The trapeze bar was made of six one-meter length pieces of soft iron pipe telescoped within the other. A single strand of insulated and electrostatically shielded wire was threaded through the innermost pipe of the bar and fastened at two places in the ceiling of the laboratory in such a manner as to permit the trapeze to swing horizontally in a North-South direction while the supporting wires on each side moved in the magnetic meridian and therefore could cut no magnetic flux. The shielded wire was connected to a sensitive wall galvanometer which was also shielded. Here again we have only the isolated motional electric field involved, for it is well known that the iron pipe would completely screen out the earth's magnetic field from the interior. With this simple apparatus, it ca be readily demonstrated that any small horizontal movement of the bar causes a deflection of the galvanometer directly proportional to its velocity. No measurable magnetic flux exists within the innermost pipe, but the electric field Vx B is present without diminution, and uncancelled by the equal and oppositely directed electrostatic field set up by the separation of charge in the shield. The wire in the pipe cut the vertical component of the earth's magnetic field, but was at rest with respect to the bar. The deflections of the wall galvanometer for a given speed were identical with or without the iron pipe and electrostatic shielding around the wire in the trapeze bar.
The Aluminum Box Experiment
In this experiment the entire apparatus was contained in a closed aluminum box which was moved horizontally in a North-South direction on a laboratory table. The test coil was rectangular in shape, made up of many turns of fine, flexible, insulated copper wire. The North and South sides of the rectangular coil were rigidized and supported in the same horizontal plane within the box. The South side was fastened to the inside South wall of the aluminum box and the terminals of the coil were connected to a sensitive portable galvanometer also mounted on this wall so that the pointer could be read through an opening in the box. The North side of the coil was supported in a fixed position by two plastic rods which were clamped to fixed vertical support rods on the table, and extended horizontally through holes in the aluminum box. The flexible East and West sides of the test coil hung in the magnetic meridian of the earth's field. Any movement North or South of the box thus caused these wires to either sag or become taut respectively. The presence of the uncancelled motional electric field can be demonstrated to be existent in the test coil when the box is completely closed and moved with various speed, North or South, across the earth's vertical magnetic field component. The deflections of the galvanometer with various speeds of the box are identical with those obtained when the shielded box is eliminated from the experiment and just the south side of the coils and the galvanometer were moved as before.
Summary
Let us make a brief summary of what we have thus far presented with respect to the motional electric field. Mathematical, operational, theoretical and experimental evidence convincingly confirm the concept of the motional electric field as physically real and distinctly unique. Its magnitude varies with reference frames in a manner unlike the electrostatic field. The crux of the theoretical argument involving this field amounted to the fact that the direct transfer of kinetic energy from a prime mover to a charged particle can be logically traced in detail and in accordance with known laws, and fully accounts for all energy transfer, whereas the conception of motional electric field energy existing at all and being distributed spatially, in addition to being capable of transfer, is next to impossible. The crucial evidence of uniqueness is experimental and it has been shown that this field does not obey Poisson's Fundamental Law of Electrostatics with respect to shielding. If the magnetic field has no physical reality, then when the motional electric field was balanced against an equal and opposite electrostatic field, the magnitude of the two terms in Equation (5) of the "New Electrodynamics" would have been identically equal and opposite and their algebraic sum equal to zero. The foregoing experimental evidence requires a concept of something real to account for the real difference experimentally measured. The magnetic field and the motional electric field concepts constitute that "something of fundamental physical significance" which was intentionally but ill-advisedly omitted in the new formulation in terms of particle electrodynamics.
Upon the foregoing evidence we rest our case that this motional field is unequivocally a unique electric field possessing its own nature, behavior and properties. We have asked nature a question and the reply is clear and unequivocal. Quantitative and qualitative experimental evidence such as has been carefully obtained in this case always has the last word. It closes the door on controversy and opens it wide toward the dawn of new horizons. Nature herself has given the answer which, in the words of Enrico Fermi, should "indeed be of great significance and consequence" to our scientific knowledge. The implications and consequences of this discovery will be discussed more fully later. They do, however, lead us immediately to the necessity for making inquiry into the basic nature of the analogous motional V x E/c magnetic field. This we will do in the next chapter.
The Motional Magnetic Field
The classical belief that nature has provide us with one and only one magnetic field has so befuddled reason that physicists have sought to eliminate the magnetic field concept entirely. To illustrate the ambiguity, the magnetic field arising from two operationally different sources will be described. The impossibility of these two fields beings identically the same becomes apparent upon comparison:
(1) The magnetic flux arising from the steady flow of electricity in a solenoid can be measured in intensity and in spatial energy content at any point in the surrounding space by an observer, either at rest or in motion with respect to the solenoid.
(2) The second source can best be described by a quotation from Sir Arthur Eddington:
"Consider an electrically charged body at rest on the earth. Since it is at rest, it gives an electric field, but no magnetic field. But for the nebular physicist it is a charged body moving at 1000 miles a second. A moving charge constitutes an electric current which in accordance with the laws of electrodynamics gives rise to a magnetic field. How can the same body both give and not give rise to a magnetic field? On the classical theory we would have to explain one of these results as an illusion. On the relativity theory, both results are accepted, magnetic fields are relative." (35 ~ A.S. Eddington: The Nature of the Physical World, p. 22, Macmillan Co., 1929)
The magnetic field arising from the solenoid is obviously born by the cooperative relative motion between unlike electric charges, such as the flow of negative electrons past the positively charged atoms in a copper wire. This type of magnetostatic field intensity is given the symbol Hs and is identified in Maxwell's equations by Curl Hs = J where J is the current density. B = mu Hs. Mu is the permeability (mks units).
The second type identify by the symbol Hm and arises wholly from relative motion v with respect to electric charges. This intensity Hm = V x Dc = EV x Ec (mks units) where E [Epsilon] is the permitivity, and Dc = EEc.
That the two magnetic fields Hs and Hm cannot possibly be identical in nature is proved mathematically as in the case of the Ec and the Em electric fields. The general mathematical expression for these two fields are obtained from the Einstein transformation equation (5) in free space where B = H in absolute gaussian (cgs) units as follows:
(Eq. 14) H's = B's = ?Hs
and
(Eq. 15) H'm = B'm = ?V x Ec
where ? = 1/?l - (v/c)2 and c = 3 x 1010 cm/sec.
Inspection shows that if the two magnetic fields H's = ?Hs
and H'm = ?V x Ec
were parallel and balanced against each other, for constant values of Es and Ec, there is one and only one possible value of v for which these two fields would have the same numerical value. In other words, if they were balanced against each other in one reference frame, they would immediately be out of balance and could not possibly cancel each other in any other frame of reference. Hence they cannot possibly be the same kinds of magnetic field, because they behave differently with change in reference frames.
Because Hm = V x Ec is a magnetic vector directed at right angles both to V and Ec, the electric field Ec can do no work, since any displacement of a magnetic particle will be a deflection at right angles to this field. The Hs magnetic field, however, can impart energy directly to a magnetic particle from its field energy.
The two types of magnetic fields described above have such obvious dissimilarities that the only possibility of a consistent satisfying picture of them is obtained by the application of Bridgman's Operational Viewpoint. When this is done we see these fields as unique. The first type Hs is analogous to the Coulomb electrical field Ec in that it has physical reality, and has a spatial distribution of magnetic energy ?H2/8? ergs/cm3
. The motional magnetic field Hm is analogous to the Em field in that it too disappears when there is no relative velocity.
The intimate relationship and unity between electricity and magnetism is seen in these two fields. The motional electric field can be described as a magnetic deflection phenomenon produced on moving charges, and the motional magnetic field can be viewed as an electric field deflection which will act on moving magnetic poles.
One of the thrills of this research project was predicted by Bridgman when he wrote, "In this self-conscious search for phenomena which increase the number of operationally independent concepts, we may expect to find a powerful systematic method directing the discovery of new and essentially important physical facts." (36 ~ ibid., p.224)
It is worth our while to note that we have six such unique field concepts shown on page 11 instead of the classical two, or the modern particle dynamics with none! These new field concepts when understood in connection with the equations of modern electrodynamics completely eliminate the paradoxes and ambiguities which have plagued this subject for years and explain electromagnetic induction which particle electrodynamics cannot handle. Most of all, they open up new horizons for the unification of the three great fields of electricity, magnetism and gravitation
Gravitation
"In the limited nature of the mathematically existent simple fields and the simple equations possible between them, lies the theorists' hope of grasping the real in all its depths." (37 ~ Albert Einstein: Essays in Science, p. 110; Philosophical Library, NY, 1934)
"It may well be that the approach of a new theory cannot begin until the mathematical nature of the old ones is clearly understood." (38 ~ Freeman J. Dyson: Scientific American, September 1958)
In the previous chapter we have shown how Bridgman's Operational Viewpoint applied to our "existent simple fields and the simple equations possible between them" has enabled us to gain an understanding of "the mathematical nature of the old" classical equations of electrodynamics which were beset with limitations, ambiguities, and paradoxes.
In order to obtain correct answers to our problems, it has been taught us that they must be analyzed operationally (40 ~ This becomes self-evident to anyone who will review the publications already cited, referring to Cohn, and to Moon and Spencer) to determine the particular types of fields that are involved, and the particular formulae among the six field types available must be selected and employed for the solution. The properties of each field type must be taken into consideration in working out problems. This clarified, straightforward procedure, working with unique field types, affords present possibilities that were not available to Einstein, due to mental doors which were closed.
It was without question Professor Einstein's life ambition to find the link between the gravitational field and the phenomena of electricity and magnetism. The reason for his failure appears now to be transparent in the light of this thesis. Most interpreters of his special theory, including Einstein himself, recognize the existence of but one electric field, in spite of the fact that Sir James Jeans has pointed out that such an interpretation of the terms in the transformation equation of his theory is not required by the postulates of the theory itself. (41 ~ J. H. Jeans: The Mathematical Theory of Electricity & Magnetism, p. 606, Cambridge Univ. Press, 1923)
In the English translation of his volume, Mein Weltbild, Einstein makes several very pertinent remarks which bear upon this thesis:
"It would of course be a great step forward if we succeeded in combining the gravitational field and the electromagnetic field into a single structure. Only so could the era in theoretical physics inaugurated by Faraday and Clerk Maxwell be brought to a satisfactory close." (42 ~ Albert Einstein: Essays in Science, p. 19; Philosophical Library, NY, 1934)
In this chapter we deal with one of the "simple fields" which has been known for years and universally employed in the generators of our electrical power plants, the unique nature of which has been unrecognized and its usefulness only partly exploited.
The greatest hurdle to be overcome in attempting to link gravitational force with any of the other known field forces of nature, is that property of gravity which enables it to act without apparent diminution in and throughout all kinds and combinations of matter. Insofar as we are aware there is no kind of matter which acts as an effective reflector or absorber of this force.
Let us now review the results of the experiments described in Chapter 3, the Ironing Board Experiment, the Trapeze Experiment, and the Aluminum Box Experiment. In all of these experiments the motional V x B suffered no diminution by virtue of the kinds of electrostatic shielding employed (i.e., iron, aluminum, brass, aquadag). We knew with certainty where the seat of action of the induced motional electric field was localized in these experiments. The behavior of this field in these experiments, therefore, has aspects which are exactly similar to gravity. Even when the resultant B itself is reduced to zero, VxB exists unaltered! No other force exists, to our knowledge, with such an unalterable and penetrating nature except that of gravity!
With the experimental evidence of the fact that the V x B field can in no instance be shielded from a region of space by a conducting shell and that it does not possess the properties of an electrostatic field, as has been tacitly assumed by theoretical physicists without experimental evidence to support it, we are brought face to face with the fact that this V x B field is really something entirely different than it has been hitherto thought to be, in spite of the fact that it is the generating field so active in our electrical power plants. Indeed it will be shown that this field should behave in a manner that is identical to gravity.
Let us remember that this VxB field is an electric field, that is, it will exert a force on, and will cause the acceleration of electric charges. In this respect it is similar to an electrostatic field. But an electrically neutral conductor places in a VxB field is acted upon differently than when it is places in an electrostatic field. In the latter field only an outside surface redistribution of charge and field take place whereas in a VxB field the neutral conductor experiences an internal redistribution of charge throughout its entire interior with two types of electric fields existent within the interior, balanced against each other in the equilibrium state. This state of affairs has been experimentally verified in the writer's laboratory and this evidence is the crucial blow which overthrows the popular view that the VxB field is electrostatic in nature. In the electrostatic case the field is entirely on the outside of the conductor, whereas in the VxB case, this field exists both within and without the conductor.
Within a conducting enclosure which is placed in an electrostatic field, this field is well known to be self-cancelled, whereas when placed in a motional electric field, this field gives rise to what has been thought to be a canceling electrostatic field equal in magnitude and oppositely directed, but contrary to popular belief this motional electric field is uncancelled by this induced electrostatic field and remains undiminished in intensity and in balance with it. This immunity to cancellation by shielding is the property which it has in common with gravity.
It is the pene
